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Preheat oven to 325u00b0. Butter two 9-in. cake pans; set aside.
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Make cake: In a large bowl, sift together flour, baking powder, and salt. Set aside. In the bowl of a stand mixer, beat butter and sugar together on low speed until light and fluffy. Add egg whites in 3 batches, scraping inside of bowl as needed. Beat in flour mixture in 5 batches, adding 1/4 cup water after each addition (you will begin and end with flour); make sure flour is completely blended each time before adding water. Pour batter into prepared pans, dividing evenly. Smooth tops with a spatula.
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Bake until center of cake feels firm to the touch and a toothpick inserted in center comes out clean, about 40 minutes. Cool cakes completely in pans on a rack.
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Meanwhile, make cranberry filling: Combine 3 cups cranberries, the sugar, preserves, and 1/4 cup water in a small saucepan and cook over high heat until cranberries pop and preserves melt, 5 to 10 minutes. Add remaining 3/4 cup cranberries, stir to combine, and remove from heat. Transfer to a small bowl and chill until ready to assemble cake.
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Make buttercream: Fill a 2-qt. pan with about 1 in. water and bring to a simmer over low heat. Put egg whites, salt, and sugar in the bowl of a stand mixer and whisk to combine. Place bowl over hot water, making sure bottom of bowl isn't touching water, and heat whites, whisking constantly, until hot to the touch, 3 to 5 minutes. Remove pan and bowl from heat.
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Put bowl of warm whites on the mixer and whisk on high speed until tripled in volume and side of bowl is cool to the touch, about 10 minutes.
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Meanwhile, chop 4 oz. white chocolate, put in a medium metal mixing bowl, and set in same pan of warm water off the heat to melt slowly, stirring occasionally. Remove bowl from pan and let cool to room temperature.
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Reduce mixer speed to low and whisk butter into whites, about 1/4 cup at a time, until incorporated. Continue to whisk on low speed until smooth and fluffy, about 10 minutes (mixture may look grainy at some point but will come together).
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With a rubber spatula, gently fold melted chocolate into buttercream until completely combined.
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Assemble: Rub tops of both cakes gently with your hands to remove browned outer surface, then carefully invert cakes and rub undersides so that cakes are completely white. Place 1 cake layer on a cake stand or serving plate, top side up. Using a pastry brush, brush top with half the liqueur. Spread about 1 1/2 cups cranberry mixture over layer with a metal spatula, leaving a 1/2-in. empty border around edge. Place second cake layer on top, flattest side down, and brush with remaining liqueur. Spread top and sides of cake with a thin layer of buttercream to seal in crumbs and chill 30 minutes. Cover with remaining buttercream, starting with the sides and covering the top last.
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Use the palm of your hand to warm remaining chocolate. Shave smooth side of chocolate bar with a vegetable peeler to make thin curls; scatter curls over cake's top. Sift powdered sugar over cake. Serve with remaining cranberry mixture on the side.
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Make ahead: Baked cake layers can be wrapped in plastic and stored at room temperature or in the fridge up to 2 days ahead. Cranberry filling can be made up to 2 days ahead and chilled.
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Bakers' tip: To make a pure white cake, use your fingers to rub off the browned surface of each layer before assembling.
